i've had that problem, it's the app. there are three options usually, go to the settings and make them something like close, reply and something else, don't use delete, it deletes them right there. i think there is a setting for it deleting them after reading as well, just fool around with the settings and you should get the results you're hoping for.

There is actually no cache to delete. It's still happening. The only way that I can see those texts is if I view it in the popup, because it never makes it to my inbox. It doesn't even show the text notification icon on those certain texts.

Hmmmm, just got the app on my shiny new d3, not having that problem. Try uninstalling and reinstalling it. Might as well give it a shot. Otherwise id try a battery pull if you haven't already, and maybe a reset if things don't go so well.